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Actris
Commits
98da017c
Commit
98da017c
authored
4 years ago
by
Jonas Kastberg
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Review comments for compute example
parent
58e53ad9
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theories/logrel/examples/compute_list_par.v
+33
-64
33 additions, 64 deletions
theories/logrel/examples/compute_list_par.v
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and
64 deletions
theories/logrel/examples/compute_list_par.v
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33
−
64
View file @
98da017c
From
actris
.
channel
Require
Import
proofmode
proto
channel
.
From
actris
.
logrel
Require
Import
session_types
subtyping_rules
term_typing_judgment
term_typing_rules
session_typing_rules
environments
telescopes
napp
.
From
iris
.
algebra
Require
Import
frac
.
From
iris
.
heap_lang
Require
Import
metatheory
.
From
actris
.
utils
Require
Import
llist
.
From
actris
.
channel
Require
Import
proofmode
proto
channel
.
From
actris
.
logrel
Require
Import
term_typing_rules
session_typing_rules
subtyping_rules
napp
.
From
actris
.
logrel
.
lib
Require
Import
par_start
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
heap_lang
Require
Import
metatheory
.
From
iris
.
algebra
Require
Import
frac
.
Definition
cont
:
Z
:=
1
.
Definition
stop
:
Z
:=
2
.
Definition
compute_service
:
val
:=
rec
:
"go"
"c"
:=
(
branch
[
cont
;
stop
]
)
"c"
branch
[
cont
;
stop
]
"c"
(
λ
:
"c"
,
let
:
"v"
:=
recv
"c"
in
send
"c"
(
"v"
#
());;
"go"
"c"
)
send
"c"
(
"v"
#
());;
"go"
"c"
)
(
λ
:
"c"
,
#
())
.
Definition
send_all_par
:
val
:=
...
...
@@ -26,19 +24,21 @@ Definition send_all_par : val :=
acquire
"lk"
;;
select
"c"
#
cont
;;
send
"c"
(
lpop
"xs"
);;
"counter"
<-
!
"counter"
+#
1
;;
release
"lk"
;;
"go"
"c"
"xs"
"lk"
"counter"
.
release
"lk"
;;
"go"
"c"
"xs"
"lk"
"counter"
.
Definition
recv_all_par
:
val
:=
rec
:
"go"
"c"
"ys"
"n"
"lk"
"counter"
:=
if
:
"n"
=
#
0
then
#
()
else
acquire
"lk"
;;
if
:
(
#
0
=
!
"counter"
)
then
release
"lk"
;;
"go"
"c"
"ys"
"n"
"lk"
"counter"
if
:
(
#
0
=
!
"counter"
)
then
release
"lk"
;;
"go"
"c"
"ys"
"n"
"lk"
"counter"
else
let
:
"x"
:=
recv
"c"
in
"counter"
<-
!
"counter"
-#
1
;;
release
"lk"
;;
"go"
"c"
"ys"
(
"n"
-#
1
)
"lk"
"counter"
;;
lcons
"x"
"ys"
.
"go"
"c"
"ys"
(
"n"
-#
1
)
"lk"
"counter"
;;
lcons
"x"
"ys"
.
Definition
compute_client
:
val
:=
λ
:
"xs"
"c"
,
...
...
@@ -63,15 +63,15 @@ Section compute_example.
Context
`{
!
inG
Σ
fracR
}
.
Definition
compute_type_service_aux
(
rec
:
lsty
Σ
)
:
lsty
Σ
:=
lty_branch
(
<
[
cont
:=
(
<
??
A
>
TY
()
⊸
A
;
<!!>
TY
A
;
rec
)
%
lty
]
>
(
<
[
stop
:=
END
%
lty
]
>∅
))
.
lty_branch
$
<
[
cont
:=
(
<
??
A
>
TY
()
⊸
A
;
<!!>
TY
A
;
rec
)
%
lty
]
>
$
<
[
stop
:=
END
%
lty
]
>
$
∅.
Instance
mapper_type_rec_service_contractive
:
Contractive
(
compute_type_service_aux
)
.
Proof
.
solve_proto_contractive
.
Qed
.
Definition
compute_type_service
:
lsty
Σ
:=
lty_rec
(
compute_type_service_aux
)
.
(** This judgement is checked only with the typing rules of the type system *)
Lemma
ltyped_compute_service
Γ
:
⊢
Γ
⊨
compute_service
:
lty_chan
compute_type_service
⊸
()
⫤
Γ
.
Proof
.
...
...
@@ -95,8 +95,7 @@ Section compute_example.
pose
proof
(
ltys_O_inv
Ys'
)
as
HYs'
.
rewrite
HYs
HYs'
/=.
iApply
ltyped_seq
.
{
iApply
(
ltyped_send
_
[
EnvItem
"v"
_;
EnvItem
"c"
_;
EnvItem
"go"
_]);
{
iApply
(
ltyped_send
_
[
EnvItem
"v"
_;
EnvItem
"c"
_;
EnvItem
"go"
_]);
[
done
|
]
.
iApply
ltyped_app
;
[
by
iApply
ltyped_unit
|
]=>
/=.
by
iApply
ltyped_var
.
}
...
...
@@ -116,8 +115,8 @@ Section compute_example.
Qed
.
Definition
compute_type_client_aux
(
A
:
ltty
Σ
)
(
rec
:
lsty
Σ
)
:
lsty
Σ
:=
lty_select
(
<
[
cont
:=
(
<!!>
TY
()
⊸
A
;
<
??
>
TY
A
;
rec
)
%
lty
]
>
(
<
[
stop
:=
END
%
lty
]
>∅
))
.
lty_select
$
<
[
cont
:=
(
<!!>
TY
()
⊸
A
;
<
??
>
TY
A
;
rec
)
%
lty
]
>
$
<
[
stop
:=
END
%
lty
]
>∅.
Instance
compute_type_rec_client_contractive
A
:
Contractive
(
compute_type_client_aux
A
)
.
Proof
.
solve_proto_contractive
.
Qed
.
...
...
@@ -125,7 +124,7 @@ Section compute_example.
lty_rec
(
compute_type_client_aux
A
)
.
Global
Instance
compute_type_client_unfold
A
:
ProtoUnfold
(
lsty_car
(
compute_type_client
A
))
(
lsty_car
(
(
compute_type_client_aux
A
)
(
compute_type_client
A
)))
.
(
lsty_car
(
compute_type_client_aux
A
(
compute_type_client
A
)))
.
Proof
.
apply
proto_unfold_eq
,
(
fixpoint_unfold
(
compute_type_client_aux
A
))
.
Qed
.
Definition
list_pred
(
A
:
ltty
Σ
)
:
val
→
val
→
iProp
Σ
:=
...
...
@@ -167,9 +166,9 @@ Section compute_example.
(
<
??
>
TY
A
;
END
)
%
lty
.
Definition
compute_type_invariant
γ
(
A
:
ltty
Σ
)
(
c
:
val
)
counter
:
iProp
Σ
:=
(
∃
(
n
:
nat
)
b
,
(
(
⌜
b
=
true
⌝
)
∨
(
own
γ
1
%
Qp
∗
⌜
b
=
false
⌝
)
)
∗
γ
(
A
:
ltty
Σ
)
(
c
:
val
)
(
counter
:
loc
)
:
iProp
Σ
:=
(
∃
(
n
:
nat
)
(
b
:
bool
)
,
(
if
b
then
True
else
own
γ
1
%
Qp
)
∗
counter
↦
#
n
∗
c
↣
(
lsty_car
(
lty_napp
(
recv_type
A
)
n
<++>
(
if
b
then
compute_type_client
A
else
END
)
%
lty
)))
%
I
.
...
...
@@ -250,7 +249,7 @@ Section compute_example.
rewrite
/
select
.
wp_apply
(
acquire_spec
with
"Hlk"
)
.
iIntros
"[Hlocked HI]"
.
iDestruct
"HI"
as
(
n
b
)
"([-> | [Hf' _]]
& Hcounter & Hc)"
;
last
first
.
iDestruct
"HI"
as
(
n
[
|
])
"(Hf'
& Hcounter & Hc)"
;
last
first
.
{
by
iDestruct
(
own_valid_2
with
"Hf Hf'"
)
as
%
[]
.
}
iDestruct
(
iProto_mapsto_le
with
"Hc []"
)
as
"Hc"
.
{
iApply
iProto_le_trans
.
...
...
@@ -264,16 +263,13 @@ Section compute_example.
wp_apply
(
release_spec
with
"[-HΦ Hl]"
)
.
{
iFrame
"Hlk Hlocked"
.
iExists
n
,
false
.
iSplitL
"Hf"
.
-
iRight
.
iFrame
"Hf"
.
done
.
-
rewrite
lookup_total_insert
.
rewrite
-
lsty_car_app
lty_app_end_l
lty_app_end_r
.
iFrame
"Hcounter Hc"
.
}
rewrite
lookup_total_insert
-
lsty_car_app
lty_app_end_l
lty_app_end_r
.
iFrame
"Hf Hcounter Hc"
.
}
iIntros
"_"
.
wp_pures
.
iApply
"HΦ"
.
iFrame
"Hl Hlk Hsf"
.
}
wp_lam
.
wp_apply
(
lisnil_spec
with
"Hl"
);
iIntros
"Hl"
.
wp_apply
(
acquire_spec
with
"Hlk"
)
.
iIntros
"[Hlocked HI]"
.
iDestruct
"HI"
as
(
n
b
)
"([-> | [Hf' _]]
& Hcounter & Hc)"
;
last
first
.
iDestruct
"HI"
as
(
n
[
|
])
"(Hf'
& Hcounter & Hc)"
;
last
first
.
{
by
iDestruct
(
own_valid_2
with
"Hf Hf'"
)
as
%
[]
.
}
iDestruct
(
iProto_mapsto_le
with
"Hc []"
)
as
"Hc"
.
{
iApply
iProto_le_trans
.
...
...
@@ -303,7 +299,6 @@ Section compute_example.
rewrite
-
lty_napp_S_r
.
rewrite
Nat
.
add_succ_r
.
rewrite
-
plus_n_O
.
iSplitR
;
[
by
iLeft
|
]
.
replace
(
Z
.
of_nat
n
+
1
)
%
Z
with
(
Z
.
of_nat
(
S
n
))
by
lia
.
iFrame
"Hc Hcounter"
.
}
iIntros
"_"
.
wp_pures
.
...
...
@@ -321,14 +316,14 @@ Section compute_example.
Proof
.
iIntros
(
Φ
)
"(Hl & #Hlk) HΦ"
.
iLöb
as
"IH"
forall
(
n
Φ
)
.
destruct
n
.
destruct
n
as
[
|
n
]
.
{
wp_lam
.
wp_pures
.
iApply
"HΦ"
.
by
iFrame
"Hl Hlk"
.
}
wp_lam
.
wp_apply
(
acquire_spec
with
"Hlk"
)
.
iIntros
"[Hlocked HI]"
.
iDestruct
"HI"
as
(
m
b
)
"(Hb & Hcounter & Hc)"
.
wp_load
.
destruct
m
.
destruct
m
as
[
|
m
]
.
{
wp_apply
(
release_spec
with
"[$Hlocked $Hlk Hb Hcounter Hc]"
)
.
{
iExists
0
,
b
.
iFrame
"Hb Hcounter Hc"
.
}
iIntros
"_"
.
wp_pures
.
iApply
(
"IH"
with
"Hl"
)
.
...
...
@@ -342,7 +337,7 @@ Section compute_example.
iExists
m
,
b
.
iFrame
"Hb Hcounter Hc"
.
}
iIntros
"_"
.
wp_pures
.
replace
(
(
Z
.
of_nat
(
S
n
)
)
-
1
)
%
Z
with
(
Z
.
of_nat
(
n
))
by
lia
.
replace
(
Z
.
of_nat
(
S
n
)
-
1
)
%
Z
with
(
Z
.
of_nat
(
n
))
by
lia
.
wp_apply
(
"IH"
with
"Hl"
)
.
iIntros
(
ys
)
.
iDestruct
1
as
(
Heq
)
"(Hl & Hc)"
.
wp_apply
(
lcons_spec
with
"[$Hl $Hw//]"
)
.
...
...
@@ -377,32 +372,7 @@ Section compute_example.
iApply
ltyped_val_lam
=>
//.
iApply
ltyped_post_nil
.
iApply
(
ltyped_lam
[
EnvItem
"xs"
_])
.
iIntros
"!>"
(
vs
)
"HΓ"
.
simpl
.
rewrite
(
lookup_delete_ne
_
"lk"
"c"
)=>
//.
rewrite
(
lookup_delete_ne
_
"lk"
"xs"
)=>
//.
rewrite
(
lookup_delete_ne
_
"lk"
"counter"
)=>
//.
rewrite
(
lookup_delete_ne
_
"lk"
"n"
)=>
//.
rewrite
(
lookup_delete_ne
_
"lk"
"ys"
)=>
//.
rewrite
(
lookup_delete_ne
_
"ys"
"c"
)=>
//.
rewrite
(
lookup_delete_ne
_
"ys"
"xs"
)=>
//.
rewrite
(
lookup_delete_ne
_
"ys"
"counter"
)=>
//.
rewrite
(
lookup_delete_ne
_
"ys"
"n"
)=>
//.
rewrite
(
lookup_delete_ne
_
"counter"
"c"
)=>
//.
rewrite
(
lookup_delete_ne
_
"counter"
"xs"
)=>
//.
rewrite
(
lookup_delete_ne
_
"counter"
"n"
)=>
//.
rewrite
(
lookup_delete_ne
_
"n"
"c"
)=>
//.
rewrite
(
lookup_delete_ne
_
"n"
"xs"
)=>
//.
rewrite
(
delete_commute
_
"lk"
"ys"
)=>
//.
rewrite
(
lookup_delete_ne
_
"ys"
"lk"
)=>
//.
rewrite
(
delete_commute
_
"lk"
"counter"
)=>
//.
rewrite
(
lookup_delete_ne
_
"counter"
"lk"
)=>
//.
rewrite
(
delete_commute
_
"lk"
"n"
)=>
//.
rewrite
(
lookup_delete_ne
_
"n"
"lk"
)=>
//.
rewrite
(
delete_commute
_
"ys"
"counter"
)=>
//.
rewrite
(
lookup_delete_ne
_
"counter"
"ys"
)=>
//.
rewrite
(
delete_commute
_
"counter"
"n"
)=>
//.
rewrite
(
lookup_delete_ne
_
"n"
"counter"
)=>
//.
rewrite
!
lookup_delete
=>
//.
iIntros
"!>"
(
vs
)
"HΓ"
.
simplify_map_eq
.
iDestruct
(
env_ltyped_cons
_
_
"c"
with
"HΓ"
)
as
(
vc
->
)
"[Hc HΓ]"
.
iDestruct
(
env_ltyped_cons
_
_
"xs"
with
"HΓ"
)
as
(
vlxs
->
)
"[Hlxs HΓ]"
.
iDestruct
"Hlxs"
as
(
l'
v
->
)
"[Hlxs Hv]"
.
...
...
@@ -415,8 +385,7 @@ Section compute_example.
iMod
(
own_alloc
1
%
Qp
)
as
(
γf
)
"Hf"
;
[
done
|
]
.
wp_apply
(
newlock_spec
(
compute_type_invariant
γf
A
vc
counter
)
with
"[Hcounter Hc]"
)
.
{
iExists
0
,
true
.
simpl
.
rewrite
left_id
.
iSplitR
;
[
by
iLeft
|
]
.
iFrame
.
}
{
iExists
0
,
true
.
repeat
rewrite
left_id
.
iFrame
"Hcounter Hc"
.
}
iIntros
(
lk
γ
)
"#Hlk"
.
wp_apply
(
par_spec
(
λ
v
,
⌜
v
=
#
()
⌝
)
%
I
...
...
@@ -431,7 +400,7 @@ Section compute_example.
iDestruct
"Hw2"
as
(
ys
)
"(-> & Hlys)"
.
iIntros
"!>"
.
wp_pures
.
iFrame
"HΓ"
.
by
iApply
llist_lty_list
.
by
iApply
llist_lty_list
.
Qed
.
Lemma
lty_le_compute_type_dual
A
:
...
...
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